With "Basic" support, I should be able to submit cases still, no?

Yep, but something has changed I believe, before you could do it via suite answers. Now you need to go in your account to account center in the tab "Support". In order to see the account center, you need to have yourself assigned the support role - even if have the administrator role.

Thanks for this - Yes, I had to give myself (the admin) the role of "NetSuite Support Center" then go to Support > Support Overview then click on NetSuite Account Center and follow links to submit a case. When you get to the submit a case screen it says that you should submit a case via SuiteAnswers... though that is no longer an option: "NetSuite recommends that you submit a support case via SuiteAnswers. It's a one-stop destination for support articles, best practices, help topics, and training videos. To Access SuiteAnswers, simply switch back to your account role, go to the the Support tab, and click on 'Go to SuiteAnswers'. Click here for more information. This form to submit a case has been updated. If you encounter any issues submitting a case from here, please file it via SuiteAnswers."

I have one account where I cannot submit support cases because I am not one of the three nominated users that can submit support cases. (although I have Administrator role & Netsuite Support Centre)